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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Closures of conjugacy classes in classical real linear Lie groups. II

Author: Dragomir Ž. Djoković
Journal: Trans. Amer. Math. Soc. 270 (1982), 217-252
MSC: Primary 22E15
MathSciNet review: 642339
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Abstract: By a classical group we mean one of the groups $ G{L_n}(R)$, $ G{L_n}(C)$, $ G{L_n}(H)$, $ U(p,\,q)$, $ {O_n}(C)$, $ O(p,\,q)$, $ S{O^{\ast}}(2n)$, $ S{p_{2n}}(C)$, $ S{p_{2n}}(R)$, or $ Sp(p,\,q)$. Let $ G$ be a classical group and $ L$ its Lie algebra. For each $ x \in L$ we determine the closure of the orbit $ G \cdot x$ (for the adjoint action of $ G$ on $ L$). The problem is first reduced to the case when $ x$ is nilpotent. By using the exponential map we also determine the closures of conjugacy classes of $ G$.

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Keywords: Classical group, adjoint representation, orbit, conjugacy class, Young diagram
Article copyright: © Copyright 1982 American Mathematical Society